Alright, I have Azura`s star and inside the soul of Almalexia. On what item should I use this for maximum benefits and what enchantment should I choose?

Check the http://www.uesp.net/wiki/Morrowind:Useful_Enchantments#More_Elaborate_Enchantments page for some suggestions. (many other ideas on that page too)

The Daedric Tower Shield is the item with the most enchanting power, at a whopping 225.

edit: It would be helpful to know what type of character you're playing, so we know what your strengths/weaknesses likely are.

I`m playing a Jack-of-all-trades. Although I am a high elf with The Apprentice sign the lowered resistance doesn`t really matter as I have nearly 1000 health. I have all the strengths and no weaknesses. I am level 100, I have 100 all attributes and skills, some even above 100. 400+ magicka.Right Fist of Randagulf (+20 str), Her left hand (+5 str), Necromancers amulet, Mentor`s ring, Marara`s ring (the one you get from the vampire), Daedric greaves with feather (From the auriel`s bow quest. I don`t really need the feather, though. I am using a mod that makes strength give me about three times more carriable weight), Boots of blinding speed, Oreyn Bearclaw`s helm, some cuirass (I can`t remember which one... but one of the artifacts... probably the dragon cuirrass). I use whatever weapon comes by... right now either Gravedigger (From Tienus), Trueflame or Hopesfire...

I am going to get Royal Signet from Helseth soon. So I`ll be more or less invincible. I`ll probably use the enchanted goblins shield aswell (heal 1 HP point per second in exchange for 50 personality).

I don`t have a robe... I have some shirt that gives me 10% magic resistance and pants with +3 personality (these are constant ofcourse). My pauldrons are not so amazing... Unenchanted Daedric left pauldron and ebony right pauldron.

for maximum points, yes, the daedric tower shield.
i like the ebony scimitar though. it's the single best 1h weapon for enchantment, only bested by
the ebony staff (which is 2h). a little hard to obtain, as the unenchanted version is only carried
by ordinators (in a specific quest i therefore edited a script, which actually removes the blade from
a dead ordinator; this is so strange: you get the entire unenchanted armor but not the blade...).
also, the blade looks cool (at least to me).

to sum it up, items to look out for is the daedric tower, the ebony scimitar and the ebony staff.
don't constant-enchant anything with almalexia's soul as this would waste the great amount of
charges from her soul.

I thought the stronger the soul, the more powerful the constant enchantment can be. Is this not so?

Nope, only the item you're enchanting determines how strong the enchantment is. For CE the strength of the soul doesn't matter, apart from having to be at least a Golden Saint or Ascended Sleeper.
http://uesp.net/wiki/Morrowind:Enchanting
Lots of information all at once.